Dual generative adversarial networks based on regression and neighbor characteristics

Imbalanced data is a problem in that the number of samples in different categories or target value ranges varies greatly. Data imbalance imposes excellent challenges to machine learning and pattern recognition. The performance of machine learning models leans to be partially towards the majority of samples in the imbalanced dataset, which will further affect the effect of the model. The imbalanced data problem includes an imbalanced categorical problem and an imbalanced regression problem. Many studies have been developed to address the issue of imbalanced classification data. Nevertheless, the imbalanced regression problem has not been well-researched. In order to solve the problem of unbalanced regression data, we define an RNGRU model that can simultaneously learn the regression characteristics and neighbor characteristics of regression samples. To obtain the most comprehensive sample information of regression samples, the model uses the idea of confrontation to determine the proportion between the regression characteristics and neighbor characteristics of the original samples. According to the regression characteristics of the regression samples, an index ccr (correlation change rate) is proposed to evaluate the similarity between the generated samples and the original samples. And on this basis, an RNGAN model is proposed to reduce the similarity between the generated samples and the original samples by using the idea of confrontation.


Imbalanced regression problem
The prediction task aims to train the model and find the mapping function y = g(x) by inputting attribute variables fx i g n i¼1 and target variables fy i g n i¼1 .And according to the formula fŷ j g m j¼1 ¼ gðfx j g m j¼1 Þ to predict the target variables fy j g m j¼1 [1,2].The task is divided into two categories the classification task and regression task correspond to temporal distribution characteristics of target values [3,4].
The imbalance of the target value of the regression sample will lead to the imbalance of the regression data.Diagram of the imbalanced regression problem is shown in Fig 1.This problem is mainly caused by the imbalance of the target value distribution of the original sample and the lack of some samples in the original sample.The distribution of the original sample target values is mostly normal distribution or skewed distribution, and some samples in the target value interval will be lost due to work errors or experimental environment limitations.These are the reasons for the imbalance of regression data.

The comparison between target value distribution of samples and test error of prediction model
We draw the distribution of the target value of the regression sample and the test error of the prediction model to intuitively show the impact of the unbalanced regression problem.We use three regression datasets to validate the universality of this effect, which includes the Abalone dataset [5] and the Airfoil self-noise dataset from UCI, the ERα_activity dataset from D of the 2021 China Graduate Mathematical Modeling Contest.The ratio of the training set to the test set is 7:3.BP is regarded as a prediction model.We split the target values of the test set into different intervals and calculate the test errors in each interval.The experimental results are shown in Fig 2. As can be seen from the diagram, the test error is large in intervals with less training data, and the test error is small in intervals with more training data.The magnitude of the test error of the prediction model is an inverse relationship to the number of samples of the training set.The comparison results prove that the imbalance of the number of samples will result in poor training effects in the minority class sample interval.The comparison results show that the test error of the prediction model is large in the sample interval with a small number of samples.

Regression characteristics of regression samples
Since the target value of the regression sample is continuous, there is a certain relationship between the adjacent samples in the probability density distribution of the target value.Using this characteristic of the regression sample, the regression sample generation model can take into account the regression characteristics of the original sample when generating the sample.This process is shown in Fig 3 .The red star represents the target value of the original sample found by the nearest neighbor idea, which is the closest to the target value of the sample to be generated.

Neighborhood characteristics of regression samples
The core idea of KNN is to predict the target value of the sample by K adjacent samples closest to the sample [6].Schematic diagram of sample neighbor characteristics is shown in Fig 4 .The model can be used for both classification and regression problems [7].When performing classification prediction, the category with the largest number (or the most weighted) of K adjacent samples is used as the predictive value of the sample; when performing regression prediction, the target value of the sample is the mean (or weighted mean) of K adjacent samples [8].
The model proposed in this paper takes advantage of the similarity between adjacent samples.This paper uses similar characteristics between adjacent samples, we first use the KNN idea to find the K samples closest to the samples to be generated and then use these samples to generate samples.Because the K samples found by KNN are the closest to the samples to be generated, the attributes and target values of the generated samples can be more corresponding, more in line with the distribution information of the original samples.
Many prior techniques have been proposed to improve the prediction effect of the machine learning model for imbalanced data.Existing solutions to address imbalanced data problems focus on the classification task.However, many datasets belong to unbalanced regression problems in reality.For example, in the field of aerospace, one needs to infer the scaled sound pressure level based on a series of indicators such as frequency, angle of attack, chord length, etc.Where scaled sound pressure level is a continuous value and highly imbalanced.For the unbalanced regression problem, there is not a lot of research to solve this problem.Current solutions are applying methods based on imbalanced classification problems directly to regression tasks.If the methods of dealing with unbalanced classification problems are used to solve unbalanced regression problems those approaches treat different scaled sound pressure levels as distinct classes is unlikely to yield the best results because it does not take advantage of the similarity between aircraft with nearby scaled sound pressure levels.Similar issues happen in medical applications.Such as ERα biological activity value related to breast cancer treatment, which is continuous and often has skewed distributions across compounds.
We have conducted research deeply aiming at the defects of current methods in the imbalanced regression problem.In order to consider the regression characteristics and neighbor characteristics of the original samples more comprehensively, and determine the proportion of the two, we add the part of the confrontation between the regression characteristics and the neighbor characteristics to the GRU model.In addition, we propose an evaluation index to measure the generation effect of the generated model.The idea of adversarial learning is used to optimize the generation effect.The main contributions of this article are as follows: • We propose the RNGRU model, which uses the adversarial idea to assign different weights to different characteristics of the sample.
• We propose the RNGAN model, which can give different weights to the sample regression characteristics and neighbor characteristics when generating samples.
• We propose an evaluation index to measure the generation effect of the generated model.

The research status of the imbalanced classification problem
For the problem of imbalanced classification, existing solutions include resampling and sample generation.

Resampling.
Many researchers hope to achieve the effect of balancing the number of samples between different classes by preprocessing the data so that the data set can be balanced before classification.Among them, sampling is the most basic method, including undersampling, oversampling and mixed sampling [9].
For undersampling, classical random undersampling refers to selecting some samples randomly from the majority class samples and forming a new training set with the original minority class samples.However, this method will lose some important sample information [10].In order to reduce the information loss caused by the under-sampling method, Lin, Weichao et al introduced an efficient method in 2017 [11].The model combined the advantages of a single multilayer perceptron classifier and C4.5 decision tree.Arefeen, MA et al. [12] proposed two novel algorithms that employ neural network-based approaches to remove majority samples that are found to reside in the vicinity of the minority samples, thereby undersampling the former to remove (or alleviate) the imbalance issue.
For oversampling, Chawla et al. [13] proposed the SMOTE algorithm in 2002.SMOTE algorithm is the most classical oversampling algorithm.The algorithm uses the nearest neighbor method to pre-set the sampling rate n, and generates a few classes of data by interpolation and adds them to the data set.The algorithm solves the shortcomings of random oversampling and easy overfitting, but there is blindness in the process of neighbor selection, and how to determine the optimal value of sampling rate n is unknown and easy to be marginalized.To solve the problem, Tao et al. [14] proposed an adaptive weighted oversampling algorithm based on density peak clustering and heuristic filtering in 2019.Unlike other clustering-based over-sampling methods, the proposed approach applies modified density peaks clustering rather than traditional k-means clustering techniques to cluster the minority instances due to its capability of accurately identifying sub-clusters with different sizes and densities, which is beneficial for the proposed method to simultaneously accommodate for between-class and within-class imbalance issues caused by various reasons.Shi Hongbo et al [15].proposed the Re-SC model.Re-SC transforms an imbalanced training dataset in the original sample space into a concatenated dataset in a new sample space.In the transformation process, Re-SC considers both the distribution of the original dataset and that of the majority of samples, thereby alleviating the loss of valuable samples and reducing the class overlapping region.
For hybrid sampling, fHU et al. [16].According to the density of the neighborhood, the mixed sampling algorithm was developed.The model divided the original data into different areas according to the density of a few samples and used different heavy sampling methods in different regions.This study proposes a new hybrid sampling set algorithm modified based on SMOTE called NASBOOST and NASBAGGING.This algorithm avoids the choice of noise samples in a minority group while maintaining diversity.Sowah, Ra et al.Based on hybrid bottom sampling technology (HCBST) [17].Most instances below the sample samples of cluster lacquer technology and the closest sampling technique of sampled sampling -based samples based on the convex combination, with more than ethnic instances, through high accuracy and accuracy and height accuracy and accuracy, accuracy and accuracy of accuracy and accuracy Sexual imbalances to solve the reliability of ethnic minorities.

Sample generation.
For models that generate samples, the most typical sample production algorithms are VAE and GAN.The VAE algorithm was proposed by Diederik P. Kingma et al [18] in 2013.The algorithm includes the encoder and decoder.The encoder is used to learn the mean and difference of the original sample and uses the decoder to generate samples that match the original sample distribution [19].Ian J. Goodfellow.etc [20,21].The proposed GAN was in 2014.This algorithm consists of a generator and is discriminatory.The purpose of the generator is to generate actual samples as much as possible to deceive the discriminator [22].The purpose of discrimination is to distinguish the samples and real samples generated by generators as much as possible.When they reach a balanced state, the performance of the generator and the discriminator is the best, and the generator can currently generate high-quality samples.Jianmin Bao et al. [23] In 2017, the CVAE-GAN model was proposed.This model optimizes CGAN's generator based on the CVAE model and makes the generated samples real and diverse.With the development of a confrontation network, some scholars have applied the GAN model in the field of zero-shooting learning, but the purpose of these studies is for specific data sets and scenes, which is not common.In order to solve this problem, To solve this problem, Yan et al. [24] The ZERONAS model with a different GAN structural search method proposes.In different cases, experiments verify the general applicability of the algorithm.In order to solve the research defects of the edge distribution of the original sample when generating the samples in the previous generation model, Meng et al. [25] The Segan algorithm was proposed in 2022.The algorithm first introduces the secondary evolution learning algorithm into the generating confrontation network model.The algorithm can improve the quality of the sample by learning the edge distribution of real data.

The research status of the imbalanced regression problem
There are some studies on the imbalance of regression issues.The current method will mainly solve the method of imbalanced classification problems directly to the unbalanced regression task.
The SMOTE algorithm classified tasks was adjusted and the unbalanced regression mission was applied in 2013 by Torgo, etc. [26].The model is called Smoter.Branco, etc. [27] Combined with insufficient sampling and over-sampling techniques, and introduced Gaussian noise into the sampling algorithm.Branco, etc. [28] A comprehensive method is proposed to handle imbalanced regression missions.However, none of these methods take into account the characteristics of unbalanced regression samples.According to the characteristics of unbalanced regression data, the label distribution (LDS) algorithm and characteristic distribution algorithm were proposed in 2021 [29].They adjusted the methods used in the imbalance of classification data and used it as a control model.Finally, the effectiveness of this method is proved.Although they proposed the corresponding solutions based on the characteristics of unbalanced regression data, they did not fully consider the information of adjacent samples [29].
The current research on imbalance regression is mainly model integration and data interpolation.Model integration does not consider the characteristics of unbalanced regression data, but directly applies to handle unbalanced classification issues on the issue of regression.Applying the data interpolation to increase the amount of information between the nearby target values increases the number of ethnic minorities samples, and does not learn the distribution information of the original sample when generating the return sample of the ethnic minorities.Although LDS and FDS methods can improve the prediction accuracy of applying classification problems to regression tasks, this method cannot comprehensively consider the sample information of neighboring samples when generating a few regression samples.

The proposed evaluation index for the quality of generated samples
In order to evaluate the quality of the generated samples more comprehensively, we propose an evaluation index of correlation change rate.The evaluation index is referred to as ccr.The calculation formula of ccr is as follows.
where ccv is the vector of the correlation between different attributes of the original sample.ccv' is the vector that generates the correlation between different attributes of the sample.n is the dimension of ccv.
The validity of the proposed index is verified by comparing the ccr between samples of the same data set and the ccr between samples that do not belong to the same data set.The experimental results are shown in Table 1.
It can be seen from Table 1 that the crr value of the same data set is smaller than the crr value between different data sets, which is consistent with common sense, that is, the samples in the same data set are more similar, and the correlation difference between different attributes in the same data set is smaller than that in different data sets.The experimental results of the three datasets are consistent with this view, which proves the universal applicability of the proposed indicators.

The proposed model
In order to learn the regression characteristics and neighbor characteristics of the original samples at the same time and give them the best weight, we propose the RNGRU model.On this basis, the regression sample generation model RNGAN is proposed by using the idea of confrontation.This section will introduce the RNGRU model and RNGAN model respectively.

RNGRU
Based on the GRU model [30], we use the adversarial idea to propose the RNGRU model, which can simultaneously learn the regression characteristics and neighbor characteristics of the regression samples and give the best weight value to both.A diagram of the RNGRU algorithm is shown in Fig 5.
Where R t and N t are the sample sets obtained by using the sample regression characteristics and the neighbor characteristics, respectively.Where b t , r t and z t is the adjustment door, reset gate and update gate.The b t is responsible for adjusting the weight of sample regression characteristics and neighbor characteristics.The larger b t represents the larger proportion of the regression characteristics of the original sample.The larger the value of z t is, the more sample information is retained at the current moment.The larger the value of r t , the more sample information of the previous moment is discarded.
The calculation formula of RNGRU model is as follows.

RNGAN
Based on the RNGRU model, we propose the RNGAN model by using the idea of confrontation.The block diagram of the RNGAN model is shown in Fig 6 .In this section, we will introduce the discriminator, prediction period and generator.[31,32], i.e., this method tries to get the generated samples and the original samples closer and closer in distribution by utilizing the method of the maximum-minimum game [33].The discriminator tries to find real samples from synthesized samples [34], and the generator tries to deceive the discriminator by generating more realistic samples [35].Concretely, network D tries to minimize the loss function: Where G(z) is the sample generated by the generator.D(x) and D(G(z)) are discriminant results of original samples and generated samples, respectively.

Predictor.
In the RNGAN algorithm, the predictor network is designed to generate regression samples with specified target values.The prediction effect of the prediction model is optimized by inputting the attributes and target values of real regression samples.The predictor network tries to minimize the loss: Where y is the target value of the original regression sample.f P is the mapping function of the prediction model.

Generator.
The generator of the RNGAN model includes the RNGRU model and BP model.The RNGRU model is responsible for learning the regression and neighbor characteristics of the original samples, and the BP model improves the diversity of the generated samples by inputting noise vectors.
For Generator 1, We learn the regression characteristics of the original sample X through the RNGRU model.We use the RNGRU model to learn the regression characteristics of the original sample X and obtain the generated sample X 1 '.For generator 2, we first input a random vector N that conforms to the standard normal distribution, and then use the BP model to obtain the generated sample X 2 '.The final generated sample X ' is shown as follows.λ 1 and λ 2 are obtained by the neural network.
During the error propagation, the error back propagation of the predictor and the error back propagation of the discriminator alternate.

Model parameters and structure
5.1.1Datasets.In this paper, the three datasets we selected belong to the three imbalanced regression models we defined respectively.These datasets include Abalone, ERα_activity, and Airfoil self-noise, covering biological, medical, and aerospace domains.We split the dataset into training and testing sets by stratified sampling.Stratified sampling can ensure that the training set and test set maintains the same distribution as the original data set.Fig  • ERα_activity: This statistics set comes from the problem of the Chinese Graduate Mathematics Modeling Competition in 2021.This dataset offers 729 molecular descriptors' organic endeavor facts and ERα of the 1974 compound, which is used to deal with ERα of breast cancer.We first selected the variables of the 729 molecular descriptors of the 1974 compounds, rating the significance of organic exercise primarily based on variables, and protecting the 20 most molecular descriptors associated with the organic activity.The authentic distribution of ERα organic undertaking is an ordinary distribution.In order to assemble a non-balanced return to the facts set, we delete 800 samples inside the vary of 5 to eight.The processing information set includes 1174 samples.The size of every container is 1.These samples have the minimal ERα organic endeavor of 2.5, and the most ERα organic exercise is 10. 10.The number of samples of every BIN modification is between two and 257.The fee distribution of the publish-processing facts set indicates substantial imbalances.The processing label is dispensed in Fig 7 (B).We can see that the processed records set belongs to the imbalanced regression records trouble of the UNIR mode.
• Airfoil self-noise: This records set is received from a sequence of air dynamics and acoustic tests.The two -dimensional wing blade fragment of the take a look at is carried out in an anal wind tunnel containing 1503 samples.The size of every trash can is 2DB.The statistics set with minimal scaling sound is 103.4DB, and the most zoom stress stage is 141DB.The range of samples for every trash can alternates between 30 and 426.The dataset suggests serious records imbalances.From Fig 7(C), we can see that the information set belongs to the imbalance of the NSIR mode.

Evaluation protocol.
In this study, we use KullBack-Leibler variations (Kl Diver-Gence), the satisfaction of the pattern generated through Manhattan distance and Chebyshev distance, and in addition consider the overall performance of exceptional strategies thru experiments.
• KL divergence: KL divergence is used to measure the distance between the two distributions.
When the two distributions are the same, their relative entropy is zero.When the distinction between the two distributions increases, their relative entropy additionally increases.Assume P(w) and Q(v) are two probability distributions on random variable w and v. Eq (12) and Eq (13) are the formulae of KL divergence in the case of discrete and continuous random variables.
• Ccr: Ccr is described as the difference of correlation coefficients between exceptional attributes in two pattern sets.This index can be used to measure the similarity between the generated samples and the authentic samples.That is the smaller the ccr cost between the generated pattern and the unique sample, the higher the era impact of the generated model.
• MAE and MSE: The suggest absolute error (MAE) represents the averaged absolute distinction between the floor fact and envisioned values over all samples.The imply squared error (MSE) represents the averaged squared distinction between the floor fact and anticipated values over all samples.The formulation is as follows.
• Pearson correlation: Pearson correlation evaluates the linear relationship between predictions and corresponding floor fact values.The formula of Pearson correlation is as follows.
where y and y ' are the true value and the predicted value.

Selection of hyperparameters.
Through experiments, we have obtained the optimal value of the step size of the regression and neighbor characteristics in the proposed model is 18, and the control experiment process is shown in Table 2.
It can be seen from Table 2 that when T is 18, the RNGAN model has a good effect on the three data sets.Too large or too small a T value will lead to a large KL divergence between the generated sample and the original sample, which will reduce the generation effect of the generated model.

Quantitative similarity comparison between samples generated by different models and original samples.
In this part, we confirm the similarity between the generated samples and the unique samples by using calculating KL divergence, Chebyshev distance, and ccr and affirm the effectiveness of the proposed mannequin by using evaluating the outcomes of special technology models.In order to keep away from accidents and make the effects greater general, we carried out six experiments, and the averaging price approach is taken on every comparison index for the three datasets.The experimental outcomes are proven in Table 3.
1.It can be viewed from Table 3(A)-3(C) that KL divergence, Chebyshev distance and ccr are positively correlated.The smaller the KL divergence is, the smaller the KL divergence, Chebyshev distance and ccr.
2. We can see from Table 3(A)-3(C) that RGAN, RVAE-GAN and RNGAN fashions are higher than the RSMOTE model.The cause for this phenomenon is that the RSMOTE mannequin actually interpolates the unique regression samples, so it is susceptible to overfitting.
3. The SMOGN + LDS + FDS mannequin has a higher technology impact than the RGAN and RVAEGAN models, which proves that by including LDS and FDS in the pattern era, the mannequin can seize the pattern facts of adjoining samples, thereby enhancing the era impact of the technology model.
4. It can be considered from Table 3(A)-3(C) that the RNGAN mannequin has a quality impact in contrast with the different 4 models.This proves that the RNGAN mannequin takes into account the regression traits and neighbor traits of the authentic pattern when producing samples, and it is beneficial to stabilize the ratio of the two by using the use of the adversarial idea.

Intuitive similarity comparison between samples generated by different models and original samples.
In order to exhibit the outcomes of unique pattern era fashions on one-of-a-kind datasets greater intuitively, we behavior PCA dimensionality discount for the unique samples and the generated samples.
The PCA (Principal Component Analysis) is an unsupervised dimensionality discount technique in desktop learning.The mannequin can keep the unique variable records to the biggest extent.PCA converts a couple of variables to fewer linearly uncorrelated composite variables through the use of orthogonal transformation and achieves the motive of variable dimensionality reduction.
In this experiment, 50 samples have been randomly chosen from the generated samples and the authentic samples, respectively.After PCA dimension reduction, samples have been decreased to two-dimensional or three-dimensional.The corresponding generated samples and unique sample scatterplots are drawn in the identical coordinate system.The test was once repeated in six instances to discover the first-class outcomes for every model, as proven in Fig 8 .1.It can be viewed from Fig 8 that the generated samples are all authentic samples after the dimension discount for RSMOTE.This is due to the generated samples of the RSMOTE algorithm being bought by way of linear interpolation of the unique samples.
2. Compared with the RSMOTE model, the RGAN, RVAE-GAN, and RNGAN fashions make bigger the range of the generated samples.Among them, the generated samples of the RGAN mannequin are large than generated samples of the RSMOTE mannequin in the variety of overlaying the authentic samples.This proves that the range of generative samples generated with the aid of adversarial thoughts is better.
3. It can be considered from the determination that the generated samples of the SMOGN + LDS + FDS mannequin are extra compared to the authentic samples in distribution than the generated samples of the RVAE-GAN model.This proves that including LDS and FDS can research the regression traits of the authentic sample.after lowering the dimensional of the generated samples and the authentic samples of the three datasets.This proves the generic benefits of the proposed algorithm intuitively.This is constant with the evaluation in the preceding section.

Comparison of prediction accuracy of different models.
In this section, we divide the lookup on the imbalance of regression records into the pattern era mannequin and expanded prediction model.In order to verify the enhancement impact of the proposed mannequin on prediction accuracy, we evaluate the brand-new lookup effects in these two instructions as manage models.
• The effect verification of the proposed model in the sample generation model In order to affirm the software fee of the proposed mannequin in practice, we teach the BP mode by using the usage of the unique samples and the generated samples.We set the education frequency to 100, and the take a look at error curve of the take a look at the set is obtained.The parameters of the BP mannequin are proven in Table 4.The proper utility impact of the RNGAN mannequin is in contrast with the RSMOTE, RGAN, RVAE-GAN, SMOGN+LDS +FDS fashions and the unique samples with the aid of take a look at error curve of the BP model.The experiments are carried out on three datasets six times, respectively, and select the first-rate results.The outcomes are proven in Fig 9. 2. It can be seen from the test error curves that the comparison effect of the error curve is consistent with the previous analysis that the four models of RGAN, RVAE-GAN, SMOGN +LDS+FDS, and RNGAN have better effects compared with the RSMOTE algorithm.
3. The era impact of the SMOGN + LDS + FDS mannequin is higher than that of RGAN and RVAE-GAN, which proves that the regression traits of unique samples can be realized via LDS and FDS.• The effect verification of the proposed model in the regression prediction model In order to further verify the effect of the proposed model, we choose the treatment method of the regression data imbalance problem that improves the prediction model as the control group.These three models are FOCAL-R, SQINV and SQINV + LDS + FDS [28].The evaluation indicators used here are MAE, MSE and Pearson correlation.The experimental results are recorded in Table 5.
1. From Table 5, it can be considered that MSE and MAE are positively correlated, and MSE and MAE are negatively correlated with |Pearson correlation|.The smaller the price of MSE and MAE, the higher the prediction effect, and the large the fee of the |Pearson correlation|, the higher the prediction effect.
2. As proven in Table 5, the SQINV mannequin after including LDS and FDS is higher than the FOCAL-R and SQINV models, because FDS and LDS can achieve the adjoining pattern records of the regression sample.
3. It can be viewed from Table 5 that the RNGAN mannequin has greater prediction accuracy than SQINV + LDS + FDS.This is due to the fact the RNGAN mannequin can use the adversarial concept to gain the top-quality percentage of the regression traits and neighbor traits of the unique sample.Compared with LDS + FDS, the RNGAN mannequin can research the pattern statistics of the authentic pattern extra comprehensively.

Conclusion
In this paper, the problem of data imbalance in regression samples is deeply studied.In order to evaluate the quality of the generated samples more accurately, we propose a ccr evaluation index, which evaluates the quality of the generated samples from the correlation between different attributes.The effectiveness of the index is verified by experiments.In order to learn the sample information of the original sample more comprehensively when generating samples, we propose the RNGAN model.The RNGRU module in the model can use the adversarial idea to obtain the optimal ratio between the regression characteristics and the nearest neighbor characteristics.Our experiments in biology, medicine and aerospace verify the effectiveness of the proposed method.
Our research brings a new direction to solve the problem of unbalanced regression.In the subsequent research, the generation effect of the generated model can be improved by constraining the correlation between different attributes.Another more challenging direction is the study of periodic time series regression samples, that is, the periodicity of the original samples is considered when generating time series regression samples.

4 .
It can be considered from Fig 8(A)-8(C) that the RNGAN mannequin has excellent effects in contrast with the different 4 fashions by means of evaluating the scatterplot distributions

Table 1 . Validation of the validity of the ccr index.
7shows the target value density distributions for these datasets.• Abalone: Abalone data set aims to predict the age of abalone measurement, and physical measurements contain 4,177 abalone physical characteristics and corresponding age.The target value is an integer between 1 and 29, and we see it here as a return data set.As described in Fig 7(A), the length of each trash can is 1 year, and the minimum age of the lowest age is 29 years.The number of samples in each box is between 22 and 2769.Major data imbalances in PSIR models and regression data that belong to imbalances.

Table 4 . BP model parameters for three datasets. Number of neurons per layer Abalone 7-4-1 ERα_activity 20-13-6-1 Airfoil self-noise 4-2-1
As proven inFig 9,the RNGAN mannequin has a fantastic impact on the 4 models, which proves that deep gaining knowledge of mannequin can extract the regression points of the unique samples greater comprehensively.5.It can be viewed from Fig 9 that the proposed algorithm has proper overall performance onimbalanced regression datasets with three modes.The experimental effects show that the proposed algorithm has well-known blessings in sensible applications.